The present invention relates generally to the stability of electric power generating systems and more particularly to a method for enhancing the transient stability of two intertied sets of three phase generators by 120-degree phase rotation.
Electric power generating systems usually consist of at least two intertied sets of three-phase generators. An example would be a remotely-located single generator set sending power over an intertie to a distant multi-generator set. Another example would be the generators in the Pacific Northwest connected to the generators in California by the Pacific Intertie. An intertie consists of at least one and preferably two or more circuits. Each circuit consists of three wires, one wire for each of the three phases of the AC current.
When one generator set has an excess of power over local load, and a second generator set has a deficiency of power over local load, the excess power can be sent over the intertie from the first to the second set. The first generator set can be thought of as synchronously turning the power deficient generators in the second set. Because of inertia-type factors, the generators in the second set lag behind those in the first set. Equivalently, the power exporting first generator set can be said to lead the power importing second generating set. This lead can be expressed as the "equivalent rotor angle difference." Since exported power can be measured by conventional means, and it is well known to be proportional to the trigonometric sine function of the equivalent rotor angle difference, the latter can be computed by those skilled in the art from the formula: P=EV sin G/X where X is the reactance of the intertie, E is the voltage at the first generator set end of the intertie, and V is the voltage at the second generator set end of the intertie. E, V, and X can be measured by conventional techniques. G is the equivalent rotor angle difference.
The value of the equivalent rotor angle difference is an indication of the stability of the system. Theoretically a system would be unstable, in the sense that synchronism is lost, if the equivalent rotor angle difference would never reach a stationary value. In practice, the system would be considered unstable when the exported power falls to some unacceptably low level after peaking, reflecting, through the previous equation, the increase in the equivalent rotor angle difference to some value past 90 degrees. The unacceptably low level of exported power could be subjectively chosen as some percentage of the maximum or peak power that could be delivered. Maximum power occurs when the equivalent rotor angle difference is 90 degrees. An unstable equivalent rotor angle difference, through the previous equation, could then be determined which can be considered as indicating imminent loss of synchronism. When this point is reached, the power company will disconnect the intertie, and there will be a power loss in the area served by the power importing second generator set. A power company might decide to disconnect the intertie before the previously determined equivalent rotor angle difference is reached if, for example, the rate of increase in that angle is excessively large. Power companies routinely determine, in accordance with the prior art, at what point they will disconnect an intertie due to imminent loss of synchronism.
Factors causing instability in a power system that previously has been operating satisfactorily are called transients. A voltage or current transient will either die out or cause the system to go unstable. The transients can be caused, for example, by a fault in the line, such as would occur when a power line transmission tower, carrying one circuit of the intertie, is knocked to the ground by high winds. This "shorted" line has dropped the electric load of the importing second generator set. This causes the exporting first generator set to speed up rotation due to the imbalance between its unchanged mechanical input and its dropped electrical load. With a double circuit intertie, power would be switched to the still standing second circuit. However, it is a question whether or not the transient can be stabilized. If the increasing equivalent rotor angle difference can't be controlled, the power company must disconnect the second and final circuit of the double circuit intertie, resulting in power loss to the importing area.
Conventional techniques known to those skilled in the art, for enhancing the transient stability of a power system include: series capacitor compensation of lines, dynamic brakes, fast valving, high-speed excitation systems, and generator and load tripping. Sometimes these controls fail to stabilize the transients.
Phase-shifting transformers can be used to improve power system transient stability, as disclosed by D. O'Kelly and G. Musgrave in "Improvement of power-system transient stability by phase-shift insertion," Proceedings of the Institute of Electrical Engineers (Proc. IEE), Volume 120, No. 2, pages 247-252, February 1973. In that article, when the equivalent rotor angle difference (which they call effective rotor angle) reaches 120 degrees (or 90 degrees), a transformer is inserted in the intertie to add a lag of 52, 60, or 40 degrees to the system. This decreases the equivalent rotor angle difference (which they call phase shifting) by 52, 60, or 40 degrees. The decreased equivalent rotor angle difference will tend to increase again, but this gives more time for the conventional stability controls to bring the system under control before synchronism is lost.
Use of a transformer to decrease the equivalent rotor angle is expensive, costing between 35 and 50 million dollars (assuming a rate of about $20 per kilowatt).
The maximum phase shift of the transformer, as discussed in the article, is 60 degrees. The article suggests that 30 or 40 degrees is more feasible. Insertion of a phase-shifting transformer puts mechanical stress on the generators, especially on the generator shafts. In the article, with a maximum 60 degrees phase shift available, a power company will have to switch in the transformer at a certain point in time. If a greater phase shift were available, then the decision to insert it could be delayed. This would allow more time for the conventional transient stability controls to stabilize the system, resulting in fewer transformer insertions and hence less damage to generator shafts. A generator shaft could cost about $50 million dollars to replace. Also, the maximum 60-degree phase shift of the prior art's transformer may not be sufficient, in some instances, to allow the conventional controls to stabilize the system.